Ideal Gas Law Calculator

Q: What is the molar volume at STP?

At STP (0°C, 1 atm): V = nRT/P = 1×0.08206×273.15/1 = 22.414 L/mol. One mole of any ideal gas occupies 22.4 L at STP.

Q: What is the R value?

R = 8.314 J/mol·K = 0.08206 L·atm/mol·K = 8.314 L·kPa/mol·K = 62.36 L·mmHg/mol·K. Match R to your pressure units.

Q: When does ideal gas law fail?

At high pressures (gas molecules touch) or low temperatures (intermolecular forces matter). Use van der Waals equation for real gases.

Q: How do I find gas density from ideal gas law?

d = PM/(RT) where M is molar mass. Higher M or P gives denser gas; higher T gives less dense gas.

Q: What is STP vs SATP?

STP: 0°C (273.15 K), 1 atm. Molar volume = 22.414 L/mol. SATP: 25°C (298.15 K), 1 bar. Molar volume = 24.790 L/mol.

The ideal gas law PV = nRT unifies all gas laws into one equation. R = 0.08206 L·atm/mol·K. Pressure in atm, volume in liters, temperature in Kelvin, and moles.

⚗️ Gas Laws📐 PV = nRT💨 Ideal Gas

n (mol)

V (L)

T (K)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Ideal Gas Law	—	PV = nRT	—
Pressure	P	nRT/V	atm
Volume	V	nRT/P	L
Moles	n	PV/RT	mol
Temperature	T	PV/nR	K
R (L·atm)	R	0.08206 L·atm/mol·K	L·atm/mol·K

Step-by-Step Examples

Example 1

Moles of Gas

Find moles in 5.00 L gas at 2.00 atm and 300 K.

n = PV/RT = (2.00×5.00)/(0.08206×300)
n = 10.00/24.62 = 0.406 mol

✓ 0.406 mol of gas

Example 2

STP Volume

1 mol of any ideal gas at STP (1 atm, 273 K).

V = nRT/P = 1.00×0.08206×273/1.00
V = 22.4 L

✓ 22.4 L/mol at STP (molar volume)

Example 3

Pressure in Container

0.500 mol gas in 10.0 L container at 25°C (298 K).

P = nRT/V = 0.500×0.08206×298/10.0
P = 1.223 atm

✓ 1.223 atm

Real-World Applications

✈️

Aeronautics

Atmospheric models use ideal gas law to predict density at different altitudes.

🔬

Laboratory Gas Calculations

All quantitative gas work uses PV=nRT to convert between P, V, n, T.

🏭

Chemical Engineering

Reactor design requires knowing gas volumes and pressures using ideal gas law.

💨

Scuba Diving

Tank pressure and gas volume calculations for dive planning.

Common Mistakes to Avoid

⚠️

R value must match units

R = 0.08206 L·atm/mol·K. If pressure in Pa: R = 8.314 J/mol·K. If pressure in mmHg: R = 62.36 L·mmHg/mol·K.

⚠️

Temperature in Kelvin always

T must be in Kelvin. 25°C = 298 K. Never use Celsius in PV=nRT.

⚠️

Ideal gas is an approximation

Real gases deviate at high P and low T. At room conditions, ideal gas law gives <1% error for most gases.

Frequently Asked Questions

What is the molar volume at STP? ▾

At STP (0°C, 1 atm): V = nRT/P = 1×0.08206×273.15/1 = 22.414 L/mol. One mole of any ideal gas occupies 22.4 L at STP.

What is the R value? ▾

R = 8.314 J/mol·K = 0.08206 L·atm/mol·K = 8.314 L·kPa/mol·K = 62.36 L·mmHg/mol·K. Match R to your pressure units.

When does ideal gas law fail? ▾

At high pressures (gas molecules touch) or low temperatures (intermolecular forces matter). Use van der Waals equation for real gases.

How do I find gas density from ideal gas law? ▾

d = PM/(RT) where M is molar mass. Higher M or P gives denser gas; higher T gives less dense gas.

What is STP vs SATP? ▾

STP: 0°C (273.15 K), 1 atm. Molar volume = 22.414 L/mol. SATP: 25°C (298.15 K), 1 bar. Molar volume = 24.790 L/mol.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

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